Somebody who is "belligerently wrong" prolongs an argument even after its obvious that their facts are wrong, their reasoning is wrong, and the point they're trying to prove isn't clear. The "belligerently wrong" will usually repeatedly change their strategy so as to prevent the conversation from actually ending. It is unclear whether the belligerently wrong are actively trolling or merely unintelligent and unwittingly causing a ruckus.

"Joe was being belligerently wrong - he kept trying to argue that the capital of Maine is Delaware, even after we linked him to a list of state capitals and pointed out that Delaware is a state in and of itself."